Stock Returns


BUSI 721, Fall 2022
JGSB, Rice University

Kerry Back

Daily Returns

  • Let’s compute close-to-close daily stock returns. Let Pt denote the price at close on day t.

  • If there are no dividends, then the gain on day t is Pt - Pt-1.

The return per $1 invested in a share at close on t-1 is

\[(P_t - P_{t-1}) / P_{t-1}\]

What about dividends?  CVX in Fall 2021



Nasdaq’s statement

Chevron Corporation (CVX) will begin trading ex-dividend on August 18, 2021. A cash dividend payment of $1.34 per share is scheduled to be paid on September 10, 2021. Shareholders who purchased CVX prior to the ex-dividend date are eligible for the cash dividend payment.

Three Dates:

  • August 18: (begins trading ex-dividend)
  • August 19: (shareholders of record receive the dividend)
  • September 10: (dividend is paid)

Ex-dividend days

  • If you buy on Aug 18, you are not entitled to the dividend.

  • Purchase Aug 17 or before (and hold through Aug 17)

    • → will be shareholder of record on Aug 19
    • → receive dividend on Sept 10

  • Why Aug 17 → Aug 19?

    • T+2 settlement

  • For computing returns, the dividend goes on the ex day.
  • The close Aug 17 to close Aug 18 return for CVX is calculated as \((P_{\text{Aug18}} + 1.34 - P_{\text{Aug17}})/P_{\text{Aug17}}\).
  • We compound daily returns to get weekly, monthly, or annual returns:

\[ (1+r_1)(1+r_2)...(1+r_T)-1 \]


  • The weekly, etc. returns are as if the dividend was received on the ex day and reinvested in new shares.

Stock splits


If a company does an \(n\)-for-1 stock split, then each shareholder gets \(n\) new shares for each of her existing shares. Shares are worth roughly \(1/n\) as much.

Split adjusted prices


Data vendors routinely compute split-adjusted prices, scaling down old prices by the same factor for comparability to new prices.

Yahoo’s adjusted prices

  • finance.yahoo.com is a good source for data, and there are python libraries that interface with its API.

  • Yahoo’s adjusted closing prices are adjusted for splits and also adjusted for dividends on each ex date.

  • On Aug 18, 2021, the Aug 17 price was adjusted as

\[ {\hat{P}_{\text{Aug17}}}={P_{\text{Aug17}}}-1.34 \]

  • $1.34 of the value of CVX at close on Aug 17 was the value of the dividend. The adjusted price is the value without right to the dividend.

All prior adjusted prices were re-adjusted on Aug 18 by the factor

\[ {\hat{P}_{\text{Aug17}}}/{P_{\text{Aug17}}} \]

Previous price ratios are therefore unchanged:

\[ \frac{\hat{P}_{t}}{\hat{P}_{t-1}}=\frac{P_{t}}{P_{t-1}}=1+r_t \]

On ex days,

\[ \frac{\hat{P}_{t}}{\hat{P}_{t-1}}=\frac{P_{t}}{P_{t-1}-D_t} \]

CVX on Aug 18, 2021

The return calculated the usual way is:

\[ \frac{P_{\text{Aug18}}+1.34}{P_{\text{Aug17}}} - 1 =-0.0267 \]

The % change in Yahoo’s adjusted close is

\[ \frac{P_{\text{Aug18}}}{P_{\text{Aug17}}-1.34} - 1=-0.0271 \]

Getting Returns from Yahoo


Install pandas-datareader or, on colab, upgrade it.


!pip install --upgrade pandas-datareader

from pandas_datareader import DataReader as pdr

price = pdr('cvx', 'yahoo', start=2010)['Adj Close']
ret_daily = price.pct_change()

Compounding Yahoo returns


Can get monthly or annual return as % change in monthly or annual Yahoo-adjusted closing prices - equivalent to compounding Yahoo daily returns.


price = pdr('cvx', 'yahoo', start=2010)['Adj Close']
ret_monthly = price.resample('M').last().pct_change()
ret_annual = price.resample('Y').last().pct_change()

# change datetime to monthly or annual (optional)
ret_monthly.index = ret_monthly.index.to_period('M')
ret_annual.index = ret_annual.index.to_period('Y')